Part 4

We may, for instance, make a measurement of the distance between Neptune and the sun according to Euclidean geometry, obtaining a certain result. But if we were on another planet and there chose a reference frame which has a wholly different relative velocity to the frame of reference which we used here on earth, and with this new reference frame we measured the identically same space between Neptune and the sun we would obtain a very different result. Which measurement would be correct? Neither would be correct if by that term we mean the absolute distance if the universe were motionless and unwarped by matter.

Hence in measuring great distances involving enormous velocities we cannot ignore the principle of relativity and hope to obtain universally accurate results. It is because of this oversight that Euclid’s geometry is found to be inadequate in such cases. But as already suggested, there is a geometry that is universal in its application, in which time enters as a fourth dimension. The measurements taken according to such a geometry do not, therefore, represent distance merely, but a blending of distance and time. This is the geometry which Einstein employs. It will be discussed in greater detail further on.

=The Special Theory of Relativity=

We will now consider Einstein’s original theory of 1905, which has subsequently been called the “Special” or “Restricted” Theory of Relativity, before attempting an examination of his “General Principle” which he announced ten years later. By so doing we will find it a stepping stone of much worth, leading us naturally to the General Theory which will be discussed later.

The Special Theory is summarized in two postulates (propositions), one relating to uniform, straight-ahead motion, and the other to the velocity of light rays. It is the combination of these two propositions that necessitates the interrelation of time and space. If both are true, and the weight of evidence seems to be on Einstein’s side, then the space-time geometry already alluded to must be correct. In any event our new conception of space and time as heretofore mentioned has doubtless prepared our minds to appreciate the postulates which we will now paraphrase in non-technical terms as follows:

(1) EVERY LAW OF NATURE MAY BE STATED IN A FORM WHICH WILL HOLD GOOD BETWEEN ALL OBSERVERS AND OBJECTS PROVIDED THE OBSERVERS AND OBJECTS ARE EACH MOVING IN A STRAIGHT LINE AND WITH UNIFORM VELOCITY; AND UNDER THESE CONDITIONS NO OBSERVER COULD POSSIBLY DETECT HIS OWN MOTION BY ANY LOCAL EXPERIMENT WHATSOEVER, UNLESS HE MAKES REFERENCE TO OBJECTS OUTSIDE HIS OWN MOVING SYSTEM.

(2) LIGHT RAYS IF UNOBSTRUCTED HAVE AN OBSERVED CONSTANT VELOCITY IRRESPECTIVE OF THE RELATIVE VELOCITY BETWEEN THE OBSERVER AND THE SOURCE OF LIGHT.

On the surface there is nothing unusual about the first postulate; it appears to be simply another way of setting forth the mechanical principle of relativity announced by Newton. But it really involves more than that, because so long as we regard all bodies and measured lengths and times as rigid and unchanged by the motion of our reference frames, then it is not true that every law of nature holds good between observer and objects as set forth in the postulate. Electro-magnetic laws, for instance, are an exception, for they really do change their form in proportion to the relative motion of our reference frames.

This first postulate simply demands a restatement of the laws of nature to make them harmonize with the principle of relativity in toto. As already observed, many inconsistencies arise in regard to time, distances and dimensions if we hold to our old conceptions that units of time and of lengths are absolute quantities which cannot vary under any circumstance or condition. We know by experiment that they do vary, hence the need of a restatement of nature’s laws to account for the facts resulting from motion. This postulate, however, concerns only one kind of motion, viz., uniform and rectilinear motion. Rotating and accelerated and generally irregular motions are dealt with under the General Theory which will be considered later.

=Laws of Nature Not Unalterable=

In this connection it is well to bear in mind that a “law of nature,” as the term is commonly used, is not some God-given formula that cannot be altered. It is but a human description of the operation of nature, based on observed facts. As our powers of observation and knowledge increase it sometimes occurs that our “laws of nature” are found to be inadequate and need revision. That is precisely what Einstein calls for. In mathematics we may stipulate that “things equal to the same thing are equal to each other,” but physically speaking the phrase is wholly ambiguous. Things observed to be equal while in uniform relative motion lose their equality when their velocities vary.

It will be noted that Einstein in his first postulate also specifies that when an observer is moving straight ahead at uniform velocity he will be unable to detect his own motion and will believe himself to be at rest unless he performs an experiment on some outside object that is not moving along with him. The truth of this is apparent to anyone who has been aboard a smoothly running train while entering or leaving a station, and has been unable to determine whether it is his train or the train on the next track that is in motion, or both, until finally his train ceases to move uniformly and he experiences a jolt as it suddenly comes to a halt, or is thrown against the back of his seat as it begins to speed up. Or perhaps while the train was moving uniformly he performed an observational experiment on some outside object, such as a house or a telegraph pole, and thereby arrived at the conclusion that his train is moving rather than the one alongside it.

Similarly we on earth are prone to consider ourselves as at rest and the heavenly bodies as moving around us, and for untold centuries mankind never stopped to question that conception. Even since we have come to know that we are merely one of the millions of rotating heavenly spheres which go to make up a universe, we are disinclined to admit that ours is not in some sense a favored position, or that an earthly reference frame is not somehow intrinsically better. But reflection convinces us that this is not so; and since it is not so, we would do well to put our science on a universal rather than upon a purely local basis by altering whatever age-old conception is necessary to make it agree with the principle of relativity.

=Paradoxical Behavior of Light=

It is the second postulate rather than the first that is astounding, because it substantially states that light rays from a given source will reach an observer who is running away from the rays just as quickly, i. e., at the same velocity, as they would reach another observer who is moving toward the rays. If an explosion should take place on the sun at this moment it would, of course, take the light about eight minutes to reach the earth, traveling at a constant velocity of 186,300 miles a second. Einstein’s declaration is that if two observers are on opposite sides of the rotating earth, one revolving away from the sun and the other revolving toward it, the instruments of each observer will indicate that the rays from the flash are traveling past him at exactly 186,300 miles a second regardless of whether he is traveling toward or away from the sun.

Ordinary concept would assume that in the one case the observer’s own velocity toward the sun should shorten the time it takes the light to reach him and thereby make it appear to him that the light is traveling faster than 186,300 miles a second, while in the other case we would suppose that the observer’s instruments would indicate that the light is traveling slower than 186,300 miles a second due to his own velocity away from the sun which should lengthen the period of transit of the rays in overtaking him. But actual experiment appears to contradict this and to corroborate Einstein’s postulate, paradoxical though it seems to our accustomed concepts. Only by viewing the universe as a four dimensional (not as a three dimensional) continuum can the matter be understood.

It is not, of course, any more strange that when light waves once start on their journey, the velocity of those waves would thereafter be unaffected by the movement of the source from which they originated, than that waves of water would not be increased or retarded by any forward or backward movement of the ship after the waves have been started on their course across the lake. Newton knew that the velocity of light past an observer is not increased by reason of the source of light moving toward the observer. But what he did not see was that neither is the velocity of light increased by reason of the observer moving toward the light.

In other words, after admitting the principle of relativity in a mechanical sense, practically as stated in Einstein’s first postulate, Newton then denied or at least overlooked that principle when it touched the subject of the propagation of light. Take, for instance, the case of light rays reaching us from certain distant stars. We cannot surely know whether the source of light is traveling toward us, or whether we are moving toward the source of light. Newton would say that the velocity of light would be unaffected in the first instance, but increased in the second. Einstein says it makes no real difference which way it is, because the principle of relativity is universal, all motion is relative, and the universe is so constructed that the velocity of light always appears constant to all observers irrespective of their motion or of the motion of the source of light relative to them.

If, however, we were traveling away from a given source of light at a greater velocity than light itself can travel it would certainly not be true that light, under such a condition, would register a constant velocity. But such a rate of motion is manifestly impossible of physical attainment, light being considered to possess the maximum velocity greater than which no material body can travel. In other words, 186,300 miles a second is the limiting velocity beyond which physical phenomena does not reach, because all matter would evidently suffer complete dissolution, being reduced to the state of free electrons, by the time such a velocity would be attained. Light is matter in the free electronic state, and the velocity of such a form of matter is known to be 186,300 miles a second, as has been stated.

Light, being a form of matter, is acted upon by gravitation. This was first demonstrated during the solar eclipse of May 29, 1919, when photographs were taken of various stars whose light at that season had to pass very near the sun in order to reach us. Three months later photographs were taken of these same stars after they had moved from their former positions. Their normal relative motion being known, it was easy to determine from the two sets of photographs whether their displacement was entirely due to that motion. It was found that their displacement was considerably less than it would have been under normal conditions, thereby indicating that the light from these stars had been deflected as it passed near the sun’s rim, making it appear to the observer that these stars then occupied positions which they did not occupy. See Fig. 3.

=Electronic Structure of Matter=

Light and electricity both travel at the same velocity, and in the final analysis they are the same form of matter. All ponderable matter is made up of molecules, and molecules consist of atoms of varying elements, except where the substance is elementary throughout, in which case the molecules are made up of a certain number of atoms of the same element. An atom is an aggregation of negatively charged particles of electricity, called electrons, which revolve and vibrate at enormous rates around a central nucleus of “protons” carrying a positive charge. If we conceive of a handful of sand as whirling around and around at such an enormous velocity as to appear as a globe several feet in diameter we have a visualization of the ultra microscopic atom and its comparative dimension to that of the individual electrons and protons which compose it.

Electrons and protons are manifestly identical in all form of matter, but all atoms do not contain the same number of them. An atom of hydrogen contains only one electron and one proton, while atoms of heavier matter contain a vast number. It is the number of electrons and protons per atom, together with their respective vibratory rates, that constitute the difference between elements. Hence every known form of matter, if reduced to the electronic state, would be found to consist of the same original stuff. Light, therefore, may be termed free electrons, i. e., electrons which are not bound into atoms, and consequently glide off in every direction at the highest possible velocity of which matter is capable, viz., 186,300 miles per second.

Thus it may be seen that all other forms of matter, since they consist of electrons in the atomic or “bound” state, could not possess a velocity equal to that of free electrons. But electrons do not become “free” simply by reason of matter undergoing a change of form. Water, for instance, may be changed into a solid (ice) or into gas (steam), but the electrons continue to revolve around their nucleus in true atomic order, and the atoms continue to hold together in the molecular state, the only change being in their rate of vibration which affects the degree of elasticity between the molecules and between the atoms. Hence whether water be in the solid, liquid or gaseous state, the molecules thereof will be found intact, each consisting of two atoms of hydrogen and one atom of oxygen (H₂O).

When matter is being burned up, producing a flame or a glow of light, this phenomenon indicates that some of the electrons have been freed from their atomic condition and have started off on their journey in the form of light rays, while another portion of them remain bound as atoms but undergo a change of form, becoming either gas or ashes.

=Michelson-Morley Experiment=

Returning now to Einstein’s second postulate, that the velocity of unobstructed light rays appears to be constant to all observers irrespective of the relative velocity between the observer and the source of light. The evidence on which this theory is based was first produced by Michelson and Morley in 1887 who at that time undertook an experiment to ascertain if possible the velocity of the earth relative to the ether. The experiment revealed that light registers a constant velocity, whether it travels in the direction of the earth’s rotation, or against the rotation, or at right angles thereto. The experiment was repeated many times with different apparatus and under various conditions, but always with the same result.

It is interesting to note the details of this experiment. Light is known to travel in waves, because rays coming against each other from opposite directions can be made to “interfere” in precisely the same manner as waves in water. If waves in the ocean come together from different directions, one of two things will happen; they will either unite and produce a larger wave, or else they will strike in a manner to measurably kill off both waves. If the crests of the two waves coincide they reinforce each other, but if they strike at right angles, the destruction of the wave motion results. This is called “interference.”